U.S. Pat. No. 8,210,165 B2 to Forrester, et al.
Depending on the angle of incidence, some ray paths through radial Fresnel lenses will be blocked by an adjacent prism's tip. In other cases, the prism tip may not be fully filled with light, as the groove height of the previous prism leads to rejection on the prism's back. Rays missing the absorber due to blocking losses LB, or to unused tip losses LU, along with transmittance losses, τ, from first order reflections contribute to the total solar energy loss for these types of concentrators. The optical performance, or geometrical loss, is measured in terms of an optical efficiency, η, stating the ratio of solar rays hitting the absorber to the radiation incident on the outside of the lens, IIncident, isη=1−(LB+LU+τ)/IIncident  (1)
Moreover multiplying the geometrical concentration ratio C with the optical efficiency allows for a direct comparison with other types of concentrators.
For a radial Fresnel lens the flux density on the absorber can be calculated by tracing the path of incident edge rays through each of the minimum deviation prisms to the absorber. Once geometrical losses are discounted from the initial flux, an effective width, ωEffective, of the prisms accounting for tip and blocking losses can be found. Transmittance losses τ accounting for first order reflections as a function of incidence angles are also deducted. The edge (maximum) rays for any combination of incidence angles are traced, and their intersections with the absorber plane are found in a cross sectional projection, resulting in a part of the absorber plane Δd being illuminated. Depending on the distance of the prism from the absorber, a factor σ describing the spread of the refracted beam isσ=Δd cos (γ)μ  (2)
The prism's height over the absorber plane defines the cosine losses of the beam when hitting the absorber at an angle γ other than normal. Closer distance means higher flux density. A factor μ is introduced to describe this distance, normalized in respect to the lens height. This procedure is repeated for each prism i on both sides of the 2D lens. The two sides are not symmetric for any combination of incidence other than normal incidence. The resulting values are cumulated according to their location on the absorber. Thus, the flux density on any part of the absorber plane as a function of cross-sectional acceptance angle θ and perpendicular acceptance angle ψ, Δε (θIncident, ψIncident) is found asΔε(θIncident, ψIncident)=Σ−ii(ωEffectiveΔdτ cos (γ)μ)  (3)
Limitation on acceptance angles for a radial, non-tracking, Fresnel lens arises from the reduced effective prism widths due to blocking and tip-related solar energy losses common with this type of refractive concentrator design form.